OFFSET
1,2
COMMENTS
A polyomino is called n-indecomposable if it cannot be partitioned (along cell boundaries) into two or more polyominoes each with at least n cells.
MacKinnon incorrectly implies that the sequence is 1,6,44.
There is a sense in which n-decomposable polyominoes with >3n-2 cells are also uninteresting: they are precisely the "n-spiders", where an n-spider is a polyomino with a cell whose removal splits it into 4 components each with <n cells. - Peter Pleasants, Feb 18 2007
LINKS
David Applegate, Pictures of all 2-indecomposable polyominoes
David Applegate, Pictures of all 3-indecomposable polyominoes
David Applegate, Pictures of all 4-indecomposable polyominoes
David Applegate, Pictures of all 5-indecomposable polyominoes
David Applegate, Pictures of all 6-indecomposable polyominoes (gzipped)
N. MacKinnon, Some thoughts on polyomino tilings, Math. Gaz., 74 (1990), 31-33.
Simone Rinaldi and D. G. Rogers, Indecomposability: polyominoes and polyomino tilings, The Mathematical Gazette 92.524 (2008): 193-204.
EXAMPLE
The six 2-indecomposable polyominoes:
......................X.
X..XX..XXX..XX..XXX..XXX
.............X...X....X.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
David Applegate and N. J. A. Sloane, Feb 05 2007
EXTENSIONS
a(4) and a(5) from Peter Pleasants, Feb 13 2007
a(6) and a(7) from David Applegate, Feb 16 2007
STATUS
approved